For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?


Given:

Wave function, y = 3.0 sin (36 t + 0.018 x + π/4) …(1)


For x = 0, equation reduces to,


y = 3.0 sin (36 t + π/4) …(2)


w = 2π/T


T = 2π rad/36rad s-1


T = π/18


t(s)



0



T/8



2T/7



3T/8



4T/8



5T/8



6T/8



7T/8



Y (cm)



3/√2



3



3/√2



0



-3/√2



-3



-3/√2



0




In the same fashion we can also find the graph for x = 2 and x = 4, for these cases the phase will change.


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